The Socceroos made a fast start in the farewell friendly ahead of their departure for the World Cup, but fell behind to Ayanda Patosi's 13th-minute strike.
The 50,000 spectators at ANZ Stadium were relieved to see Tim Cahill, captaining the team in the absence of Mile Jedinak, equalise just a minute later.
But the home side couldn't maintain their early intensity beyond the first 30 minutes, prompting one reporter to remind Postecoglou of his stated goal since taking charge of the national team; to make people excited about watching the Socceroos.
"I didn't say that after one game did I? I think I said after the World Cup. We are still three weeks away from our first game or just under," the coach said.
"We had some objectives to work hard and try and play our gameplan. It was a bit of a struggle, but the players played it out until the end.
"It was a good initial spell for us. We struggled a little physically. With the work the players have done the last 10 days it is not really surprising. We have used this period to really work them hard as a result of that - even though they gave everything - after 20-25 minutes they really struggled physically.
"Leading into the game we've overworked them for a reason. How much of the performance was fatigue and how much was it them not grasping the game-plan? Time will tell."
First-choice right-back Ivan Franjic went off injured in the second half, prompting fears Australia may lose another important player on the eve of the World Cup, although his coach offered a cautiously optimistic assessment.
"He got a knock on his knee. I don't think it's anything serious," Postecoglou added.
"We'll wait and see what the medical team say."
South Africa coach Gordon Igesund felt the performance of his players vindicated the spirited pre-match defence he mounted following criticism of the visitors' severely weakened travelling squad.
"We achieved what we needed to achieve," he said.
"There was a lot of talk about Bafana Bafana coming here with a team that was a farce. But I thought they did very well tonight, they worked hard."
Asked what he made of Australia's chances at the World Cup after seeing them in action against his side, the visiting coach offered a diplomatic response.
"It was a funny game," he said. "The important thing is going to the tournament, your team is going and we're not and we're incredibly jealous. They'll be competitive."